# Functions-6

### From Homeworkwiki

**Let A ⊆ N and f : A → A be defined by **

**f(n) : the highest prime factor of n.**

**If range of f is A, determine A. Is A uniquely determined?**

**Solution:** For any n ∈ A, we have

f(n) = Highest prime factor of n

=> Range of f consists of prime number only

But, it is given that range of f is A. Therefore, set A consists of prime numbers only.

Hence, A = set of some prime numbers.

Clearly, A is not uniquely determined.